Solve for $x$ and $y$ using elimination. ${-3x-3y = -39}$ ${4x+y = 22}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $3$ ${-3x-3y = -39}$ $12x+3y = 66$ Add the top and bottom equations together. $9x = 27$ $\dfrac{9x}{{9}} = \dfrac{27}{{9}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-3x-3y = -39}\thinspace$ to find $y$ ${-3}{(3)}{ - 3y = -39}$ $-9-3y = -39$ $-9{+9} - 3y = -39{+9}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 3}$ into $\thinspace {4x+y = 22}\thinspace$ and get the same answer for $y$ : ${4}{(3)}{ + y = 22}$ ${y = 10}$